Define hypothesis. What are the nature, scope and testing of hypothesis?
A tentative proposal made
to explain certain observations or facts that requires further investigation to
be verified. A hypothesis is a formulation of a question that lends itself to a
prediction. This prediction can be verified or falsified. A question can only be
use as scientific hypothesis, if their is an experimental approach or
observational study that can be designed to check the outcome of a prediction.
Nature of hypothesis
The various discussions of the
hypothesis which have appeared in works on inductive logic and in writings on
scientific method, its structure and function have received considerable
attention, while its origin has been comparatively neglected. The hypothesis
has generally been treated as that part of scientific procedure which marks the
stage where a definite plan or method is proposed for dealing with new or
unexplained facts. It is regarded as an invention for the purpose of explaining
the given, as a definite conjecture which is to be tested by an appeal to
experience to see whether deductions made in accordance with it will be found
true in fact. The function of the hypothesis is to unify, to furnish a method
of dealing with things, and its structure must be suitable to this end. It must
be so formed that it will be likely to prove valid, and writers have formulated
various rules to be followed in the formation of hypotheses. These rules state
the main requirements of a good hypothesis, and are intended to aid in a
general way by pointing out certain limits within which it must fall.
In respect to the origin of the
hypothesis, writers have usually contented themselves with pointing out the
kind of situations in which hypotheses are likely to appear. But after this has
been done, after favorable external conditions have been given, the rest must
be left to "genius," for hypotheses arise as "happy
guesses," for which no rule or law can be given. In fact, the genius
differs from the ordinary plodding mortal in just this ability to form fruitful
Hypotheses in the midst of the
same facts which to other less gifted individuals remain only so many
disconnected experiences. Hypothesis is to determine its nature a little more
precisely through an investigation of its rather obscure origin, and to call
attention to certain features of its function which have not generally been
accorded their due significance.
The scope of hypothesis:
We should be surprised that
language is as complicated as it is. That is to say, there is no reasonable
doubt that a language with a context-free grammar, together with a transparent
inductive characterization of the semantics, would have all of the expressive
power of historically given natural languages, but none of the quirks or other
puzzling features that we actually find when we study them. This circumstance
suggests that the relations between apparent syntactic structure on the one
hand and interpretation on the other --- the “interface conditions,” in popular
terminology --- should be seen through the perspective of an underlying
regularity of structure and interpretation that can be revealed only through
extended inquiry, taking into consideration especially comparative data.
Indeed, advances made especially during the past twenty-five years or so
indicate that, at least over a broad domain, structures either generated from
what is (more or less) apparent, or else underlying those apparent structures,
display the kind of regularity in their interface conditions that is familiar
to us from the formalized languages. The elements that I concentrate upon here
are two: the triggering of relative scope (from the interpretive point of
view), and the distinction between those elements that contribute to meaning
through their contribution to reference and truth conditions, on the one hand,
and those that do so through the information that they provide about the
intentional states of the speaker or those the speaker is talking about, on the
other. As will be seen, I will in part support Jaakko Hintikka’s view that the
latter distinction involves scope too, but in a more derivative fashion than he
has explicitly envisaged.
TESTING OF HYPOTHESIS
Hypothesis testing refers to the
process of using statistical analysis to determine if the observed differences
between two or more samples are due to random chance (as stated in the null
hypothesis) or to true differences in the samples (as stated in the alternate
hypothesis). A null hypothesis (H0) is a stated assumption that there is no
difference in parameters (mean, variance, DPMO) for two or more populations.
The alternate hypothesis (Ha) is a statement that the observed difference or
relationship between two populations is real and not the result of chance or an
error in sampling. Hypothesis testing is the process of using a variety of
statistical tools to analyze data and, ultimately, to fail to reject or reject
the null hypothesis. From a practical point of view, finding statistical
evidence that the null hypothesis is false allows you to reject the null
hypothesis and accept the alternate hypothesis. Hypothesis testing is the use
of statistics to determine the probability that a given hypothesis is true. The
usual process of hypothesis testing consists of four steps.
1. Formulate the null hypothesis
(commonly, that the observations are the result of pure chance) and the alternative
hypothesis (commonly, that the observations show a real effect combined with a
component of chance variation).
2. Identify a test statistic that
can be used to assess the truth of the null hypothesis.
3. Compute the P-value, which is
the probability that a test statistic at least as significant as the one
observed would be obtained assuming that the null hypothesis were true. The
smaller the -value, the stronger the evidence against the null hypothesis.
4. Compare the -value to an
acceptable significance value (sometimes called an alpha value). If , that the
observed effect is statistically significant, the null hypothesis is ruled out,
and the alternative hypothesis is valid.
Flow Diagram
1 Identify the null hypothesis H0
and the alternate hypothesis HA.
2 Choose ?. The value should be
small, usually less than 10%. It is important to consider the consequences of
both types of errors.
3 Select the test statistic and
determine its value from the sample data. This value is called the observed value
of the test statistic. Remember that a t statistic is usually appropriate for a
small number of samples; for larger number of samples, a z statistic can work
well if data are normally distributed.
4 Compare the observed value of
the statistic to the critical value obtained for the chosen ?.
5 Make a decision.
If the test statistic falls in
the critical region:
Reject H0 in favour of HA. If the
test statistic does not fall in the critical region:
Conclude that there is not enough
evidence to reject H0.
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